Fermat’s last theorem, also called Fermat’s great theorem, the statement that there are no natural numbers (1, 2, 3, …) x, y, and z such that xn + yn = zn, in which n is a natural number greater than 2. For example, if n = 3, Fermat’s theorem states that no natural numbers x, y, and z exist such that x3 + y3 = z3 (i.e., the sum of two cubes is not a cube). In 1637 the French mathematician Pierre de Fermat wrote in his copy of the Arithmetica by Diophantus of Alexandria (c. ad 250), “I have discovered a truly remarkable proof [of this theorem] but this margin is too small to contain it.” For centuries mathematicians were baffled by this statement, for no one could prove or disprove Fermat’s theorem. Proofs for many specific values of n were devised, however, and by 1993, with the help of computers, it was confirmed for all n < 4,000,000. Using sophisticated tools from algebraic geometry, the English mathematician Andrew Wiles, with help from his former student Richard Taylor, devised a proof of Fermat’s last theorem that was published in 1995 in the journal Annals of Mathematics.

Learn More in these related articles:

August 17, 1601 Beaumont-de-Lomagne, France January 12, 1665 Castres French mathematician who is often called the founder of the modern theory of numbers. Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Independently of...

study of the geometric properties of solutions to polynomial equations, including solutions in dimensions beyond three. (Solutions in two and three dimensions are first covered in plane and solid analytic geometry, respectively.)

External Links

Wolfram MathWorld - Fermat’s Last TheoremAnnotated essay on this algebraic theorem proposed by this French mathematician, which consists of a Diophantine equation. Includes links to definitions of mathematical terms and relevant articles.